A non-perturbative, spatially resolved measurement of the magnetic field deep within a high temperature magnetically confined plasma is very difficult and has only been achieved under special conditions at great effort. Just once, with a carefully tailored tokamak discharge and a special sensing apparatus has the internal magnetic field been directly detected, non-perturbatively, at a single location. See “Measurement of magnetic fields in a tokamak using laser light scattering” Forrest, M. G., Carolan, P. G. and Peacock, N. J. (1978). Nature 271:718. This one-off measurement has never been repeated. The prior art simply does not provide a devices or method that can be applied routinely or under general conditions to determine the local magnetic field.
In the field of plasma physics, relevant to magnetic fusion, knowledge of the magnetic field distribution throughout the plasma volume is crucial to understanding the key issues of magnetohydrodynamic (“MHD”) stability and energy transport. Since the 1950's, a major international collaboration has developed employing many hundreds of scientists world wide to understand the dynamics of magnetic confinement of plasmas with the goal of achieving controlled thermonuclear fusion. The subject is of immense importance since the field has a direct impact on the future energy resources available to society. In this time, an experimental means of directly measuring the internal magnetic field structure has been highly sought after but has not yet been attained. Only for the well developed tokamak confinement device have multiple diagnostic systems produced detailed knowledge of the internal magnetic field structure but no direct measurements of such. The problem is that fusion relevant plasmas have temperatures of approximately 100 million° C. or greater, representing an extremely hostile environment for direct measurement techniques. The next generation of laboratory plasmas promises to be even more challenging with the addition of radiation hazards from the production of significant amounts of fusion energy and high neutron fluxes making remote sensing of plasma parameters essential. Many conventional plasma diagnostic systems cannot be adapted to the harsh radiation environment of such a plasma.
An experimental determination of the spatial variation of the magnetic field is important for a number of reasons. The knowledge of the internal magnetic field distribution is equivalent to knowing the current distribution in the plasma. Much importance is placed on measuring the mid-plane magnetic q-profile or magnetic shear from the edge to the center of the plasma. Advanced tokamak scenarios involve controlling the q-profile to stabilize destructive modes that grow and terminate the plasma discharge. At present, sophisticated equilibrium codes are used which rely on a large number of diagnostic measurements, mostly external magnetic measurements, to infer the q-profile but with poor accuracy, poor localization, and poor response time. A means of rapidly determining the q-profile, in real time, is needed for feedback purposes in order to detect the presence and location of a destructive MHD instability so that the current profile can be quickly adjusted. The magnetic shear for tokamak plasmas is typically everywhere positive; however, reversed magnetic shear discharges have lately been reported but direct evidence is lacking and magnetic profile measurements are needed. Recently, tokamak discharges with current-less cores have been reported, but again, direct evidence and profile measurements are needed. The need for a non-perturbative, spatially resolved measurement of the internal magnetic field is just as urgent and contemporary today as it was 50 years ago.
In order to gain an appreciation of the exceptional attributes of the present invention one must look at the resources and effort employed in the magnetic fusion field to determine the plasma state. The largest tokamak, the Joint European Tokamak (“JET”) project, has an annual operating budget over $100 million. The main diagnostic systems in this discipline are: arrays of external magnetic field sensors (magnetic field probes, current and flux sensors), continuous wave (“CW”) laser polarimetry and interferometry, Thomson scattering, coherent scattering, reflectometry, motional Stark effect (“MSE”), beam emission spectroscopy (“BES”), laser induced fluorescence (“LIF”), Langmuir probes, internal magnetic field probes, soft X-ray tomography, bremsstrahlung emission, electron cyclotron emission (“ECE”) and magnetic field equilibrium codes (“EFIT”). For the plasma parameters the systems address, several are perturbative, several provide chord averaged measurements, and several are indirect being measurements outside the plasma volume but none provide a direct, non-perturbative measurement of a local magnetic field B. For larger tokamak experiments, most of the above systems are routinely used and correlated to infer local plasma parameters and indirectly, the local magnetic field inside the plasma. The next generation of larger devices are designed to have higher magnetic fields and higher plasma densities which, in general, pose more problems, especially for external measurements or diagnostics using beams: LIF, MSE, and BES and for material probes: magnetic field and Langmuir probes. The purely optical diagnostics are highly favored for future devices.
A short and necessarily incomplete overview of magnetic field sensing in plasmas follows. Material probes such as magnetic pickup coils have been successfully inserted into low temperature plasmas and measure the local magnetic field quite well. On fusion relevant devices, such probes poison the plasma, perturbing the plasma even when confined to the low temperature edge. Next, the CW polarimeter diagnostic exploits the magneto-optic activity known as the Faraday effect to measure a chord averaged electron density-(parallel)magnetic field product along the probe beam. The Faraday effect is only sensitive to the component of B parallel to the path of the probe beam, B∥. The measurement is non-perturbative but non-local and the two parameters, electron density and magnetic field, cannot be separately determined. A CW polarimeter is usually combined with a laser interferometer to independently measure the chord averaged electron density along the same sightline. However the two chord averaged measurements cannot be combined to produce even a chord averaged magnetic field. Many CW polarimeter/interferometer sightlines are needed to resolve local details by tomographic means, a complex and costly proposition with a poor return on spatial resolution. Nevertheless, the CW polarimeter/interferometer diagnostic is considered essential on any large device. Today, the MSE diagnostic is being intensively pursued on mainstream tokamak devices as a viable direct measurement technique that can routinely provide local internal magnetic field measurements (q profiles). The MSE diagnostic requires a particle beam and so is perturbative. However, it has difficulty reaching deep locations in high temperature plasmas, suffers from low light levels, poor spatial and temporal resolution and its sightline is fixed to the particle beam. The MSE diagnostic is also difficult and expensive to implement and only viable on plasmas that are well understood and well diagnosed, essentially the tokamak. Lastly, magnetic equilibrium reconstruction can be used to infer the internal magnetic field distributions from magnetic field measurements (pickup coils, flux and current sensors) external to the plasma. The magnetic field is extrapolated from the outside inward. This technique is ill-conditioned only providing details just inside the plasma edge. Additional internal measurements of any plasma parameter significantly constrain the solution and inputs from all of the aforementioned diagnostics are used to more accurately determine local B. For plasmas that are not the mainstream tokamak or stellarator configurations, many of the above diagnostics are of much less utility. This is because the plasmas can be highly dynamic and transient, the plasma theory is less developed, the experimental access is different, the diagnostics are not amenable to the magnetic configuration or insufficient manpower is available. Nevertheless, these plasmas are important and are also being pursued as a means to achieve fusion energy.
The prior art that represents the present state of non-perturbative remote magnetic field sensing in plasmas is the well-known CW plasma polarimeter/interferometer instrument. That is not to say that CW plasma polarimetry/interferometry directly measures the magnetic field, far from it, but it does measure a quantity directly related to the magnetic field. The instrument measures the chord averaged electron density-(parallel)magnetic field product and the chord averaged density along a laser beam path (trajectory) through the plasma. From these two non-local measurements and assumptions about the density distribution, it is possible to draw some conclusions about the magnetic field distribution. In principle, if many such systems were employed, a local magnetic field and local density could be ascertained by tomographic means. For the required spatial resolution, such an undertaking would be out of the question, though multi-chord systems are in use.
FIG. 1 shows an isometric view of a schematic representation of a CW polarimeter/interferometer. The polarimetry part of the instrument includes, in elemental form, a light source 20, emitting a continuous polarized collimated beam 18, a directional coupler 26, and a polarization detection system 10. The CW polarimeter is sensitive to a magnetic field distribution 29 distributed in a remote magnetized plasma 28. The directional coupler 26 can be a non-polarizing beamsplitter. The light source 20 need not be coherent for polarimetry and is linearly polarized. Some fraction (50%) of the polarized collimated beam 18 is transmitted through the directional coupler 26, through the remote magnetized plasma 28, along a beam axis 24, retro-reflected by end mirror 22b, doubles back along the beam axis 24 and some fraction (50%) is reflected (redirected) by the directional coupler 26 toward the polarization detection system 10. A collimated output beam 25 is analyzed using a polarizing beam splitter 16 that spatially separates the collimated output beam 25 into two mutually orthogonal collimated analyzed output beams 15a,b. Focusing lenses 14a,b focus the collimated analyzed output beams 15a,b onto optical detectors 12a,b producing electrical signals (voltage or current) proportional to the intensity of the collimated analyzed output beams 15a,b. The rotation angle, αCW, of the polarization of the collimated output beam 25 relative to the polarization state of the light source 20 is measured. The result for a magnetized plasma with electron density distribution, ne, and magnetic field distribution, B, is given by:
                                          α            CW                    ⁡                      (            T            )                          =                  2          ×          2.63          ×                      10                          -              13                                ⁢                      λ            o            2                    ⁢                                    ∫              0              Lp                        ⁢                                          (                                                      n                    e                                    ⁢                                      B                    ∥                                                  )                            ⁢                              (                                  s                  ,                                      t                    ⁡                                          (                      s                      )                                                                      )                            ⁢                              ⅆ                s                                                                        Eq        .                                  ⁢        1            where Lp is the length (“chord length”) of the scene (“probe”) beam 23 in the remote magnetized plasma 28 and λo is the wavelength of the light source 20. For a probe beam propagating at the speed of light c(3×108 m/s), the explicit time dependence varies with location s, as t(s)=s/c. Eq. 1 can be interpreted as follows: the polarization of the probe beam rotates an angle αCW(T) in the plane of polarization for a beam path (trajectory) in the magnetized plasma parameterized by path length, s, from the plasma edge (s=0) to the opposite edge, (s=Lp),—and back again, and varies proportionally to the line integrated neB∥ product along the beam path. The time, T, is identified with the entire path integral, a duration of 2Lp/c seconds. B∥ and ne are generally time dependent but assumed constant (quasi-static) on a time scale of 2Lp/c and t(s) can be replaced by T in Eq. 1. The chord averaged rotation angle is <αCW>Lp(T)=αCW(T)/2Lp. Eq. 1 expresses the magneto-optic Faraday effect for magnetized plasmas using CW plasma polarimetry. The Faraday effect is exceptional in that the retro-reflected beam continues to accumulate rotation angle, doubling that of a single pass system. Eq. 1 is a simplified expression that assumes the frequency of the light source, νo(c/λo), is much higher than any cutoff frequency along the probe beam path. Without including interference from a reference beam 21, the optical detectors 12a,b are sensitive to the intensity in the collimated analyzed output beam 15a,b, conventionally labeled the s and p polarization channels. If the axis of the polarizing beam splitter 16 is oriented to be approximately 45° to the polarization of the light source, then the voltage difference, (Vs−Vp), for balanced optical detectors 12a and 12b varies proportionally with 2αCW(T)Io(T) for small αCW(T) and the sum, (Vs+Vp), to the total intensity, Io(T), of the collimated output beam 25. The proportionality constants are obtained from the measured responsivity (calibration) of the optical detectors 12a,b. 
Typically, a CW plasma polarimeter is combined with a CW interferometer 19 to simultaneously measure the chord averaged electron density over the same probe beam path. The interferometry part of the instrument includes, in elemental form, the light source 20, emitting the continuous coherent polarized collimated beam 18, the interferometer 19 and the phase-sensitive polarization detection system 10. The light source need not be polarized for interferometry alone. The polarimeter/interferometer shown in FIG. 1 uses a laser as the coherent light source 20 emitting the continuous coherent polarized collimated beam 18 at a prescribed wavelength and incorporates an interferometer 19 including a reference beam 21 with end mirror 22a, a scene beam 23 with end mirror 22b and the directional coupler 26 (non-polarizing beam splitter). The scene beam 23 with the beam axis 24 intersects the remote magnetized plasma 28. The directional coupler 26 redirects the beam axis 24 and combines the scene and reference beams onto the phase sensitive polarization detection system 10 comprising the polarizing beam splitter 16 which analyzes and spatially separates the polarized collimated beam 18 into two mutually orthogonal collimated analyzed output beams 15a,b, focusing lenses 14a,b focuses the collimated analyzed output beams 15a,b onto optical detectors 12a,b producing electrical signals (voltage or current) proportional to the product of the electric field amplitudes of the reference and scene beams in their respective polarization channels. A relative phase difference between the reference and scene beams, due to the index of refraction of the remote magnetized plasma, produces an interference at the optical detectors. The optical detectors act as optical mixers and both the phase and amplitude of the interference is measured. The phase difference of either optical detector is given by:
                                          ϕ            CW                    ⁡                      (            T            )                          =                  2          ×          4.5          ×                      10                          -              16                                ⁢                      λ            o                    ⁢                                    ∫              0              Lp                        ⁢                                                            n                  e                                ⁡                                  (                                      s                    ,                                          t                      ⁡                                              (                        s                        )                                                                              )                                            ⁢                                                          ⁢                              ⅆ                s                                                                        Eq        .                                  ⁢        2            Eq. 2 can be interpreted as follows: the phase difference between the reference beam and the scene beam, φCW(T), for a path in the remote magnetized plasma parameterized by path length, s, from the plasma edge (s=0) to the opposite edge, (s=Lp), varies proportionally to the line integrated ne along the path. The chord averaged phase is <φCW>Lp(T)=φCW(T)/2Lp which yields a chord averaged electron density. The time, T, is identified with the entire path integral, a duration of 2Lp/c seconds where ne is assumed quasi-constant on a time scale of 2Lp/c seconds.
For the combined CW polarimeter/interferometer instrument, the amplitudes of the interference for both s and p channels are used to determine the polarization state of the collimated output beam 25, αCW(T). The difference in the amplitudes of the optical detector voltages for balanced detectors, <Vs>amp−<Vp>amp, is proportional to 2αCW(T)Io(T) for the polarizing beam splitter 16 axis set to 45° to that of the polarization of the light source 20 and the sum of the amplitudes, <Vs>amp+<Vp>amp is proportional to Io(T), the intensity of the collimated output beam 25.
Another type of the CW polarimeter/interferometer is an instrument configured as two independent polarization sensitive interferometers operating in the right(R) and left(L) circular polarization basis, yielding the two phase measurements φR(T) and φL(T). In this case, the sum (φR+φL) is proportional to φCW(T) and the difference (φR−φL) to αCW(T). This illustrates that plasma polarimetry is, intrinsically, an interference effect and polarization sensitive interferometry is sufficient to measure both a chord averaged ne and chord averaged neB∥ product.
The CW plasma polarimeter uses a continuous linearly polarized light source of determined wavelength, λo, but the light source need not be coherent. The Faraday effect causes a progressive rotation in the polarization of the probe beam as it propagates in the magnetized plasma in the linear polarization basis. In a circularly polarized (“helicity”) basis, the Faraday effect can be viewed as a progressively increasing difference in phase between two coherent probe beams, one left circularly polarized, the other right. The two pictures can be reconciled by noting that a linearly polarized light source is the superposition of equal amplitudes of left and right circularly polarized light. In essence, the magneto-optic Faraday effect is an interference phenomenon between two coincident probe beams, one left, the other right circularly polarized, both naturally provided by a linearly polarized light source. The rotation angle, αCW, is the interference (difference in phase) between the two probe beams. The difference phase for two probe beams with the same beam path is immune to common mode phase (coherence) effects. A linearly polarized incoherent light source is sufficient for polarimetry because the necessary interfering components in the helicity basis are all naturally present in the right proportions. The difference phase, αCW, also lies in an orthogonal space (the plane of polarization) to that of the temporal phase. The λo dependence is the only connection between the temporal properties of the light source with rotation angle, αCW.
The CW plasma interferometer measures the difference in phase between the temporal phase of the scene beam and the reference beam at the optical detector. The phase measurement is subject to coherence effects since these two beams have different beam paths. The phase measurement is directly affected by the phase noise of the light source and phase noise introduced to either beam in such a way that is not common to both beams.
Another remote sensing, non-perturbative diagnostic in this field is the Thomson scattering LIDAR(LIght Detection and Ranging) instrument but this diagnostic does not exploit the polarization of the light source or contribute to the remote sensing of the magnetic field. A LIDAR Thomson scattering instrument is employed on the JET tokamak to measure the local electron density distribution, ne(s), and the local electron temperature distribution, Te(s), from the intensity and spectral distribution, respectively, of backscattered light induced by a propagating light pulse in the plasma along the light pulse beam path. The location of the measurements are given by time-of-flight and the spatial resolution is determined by the light pulse length and the response time of the optical detector. The instrument is ideal for remote sensing of ne(s) and Te(s) in future devices.